Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations

In this work, we investigate the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and nonunital channels. Herein, we choose Pauli operators \(\sigma _x \) and \(\sigma _z \) as a pair of observables of interest measuring on particle A, and the uncertainty can be predicted when particle A is entangled with quantum memory B. We explore the dynamics of the uncertainty for the measurement under local unitary (phase-damping) and nonunitary (amplitude-damping) channels, respectively. Remarkably, we derive the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under various realistic noisy environments; it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose \(\sigma _x \) and \(\sigma _y \) measurement. Besides, we find out that the entropic uncertainty will have an optimal value if one chooses \(\sigma _x \) and \(\sigma _z \) as the measurement incompatibility, comparing with others. Furthermore, in order to reduce the entropic uncertainty in noisy environment, we propose an effective strategy to steer the amount by means of implementing a filtering operation on the particle under the two types of channels, respectively. It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength. Thus, our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.     

Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments

Quantum Information Processing - Based on the NEQR of quantum images, a new quantum gray-scale image watermarking scheme is proposed through Arnold scrambling and least significant bit (LSB)...     

Quantum-memory-assisted entropic uncertainty relations under weak measurements

We investigate quantum-memory-assisted entropic uncertainty relations (EURs) based on weak measurements. It is shown that the lower bound of EUR revealed by weak measurements is always larger than that revealed by the corresponding projective measurements. A series of lower bounds of EUR under both weak measurements and projective measurements are presented. Interestingly, the quantum-memory-assisted EUR based on weak measurements is a monotonically decreasing function of the strength parameter. Furthermore, some information-theoretic inequalities associated with weak measurements are also derived.     

Conditional entropic uncertainty relations for Tsallis entropies

The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find entanglement-dependent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem 1. Taking the special case of von Neumann entropy and utilizing the concavity of conditional von Neumann entropies, we extend our result to mixed states. Finally we provide a lower bound on the amount of extractable key in a quantum cryptographic scenario.     

Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

The uncertainty principle imposes constraints on an observer’s ability to make precision measurements for two incompatible observables; thus, uncertainty relations play a key role in quantum precision measurement in the field of quantum information science. Here, our aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs. Explicitly, we explore the dynamics of the uncertainty relations via entropic measures in non-Markovian regimes when two atomic qubits independently interact with their own infinite degree-of-freedom bosonic reservoir. We show that measurement uncertainty vibrates with periodically increasing amplitude with growing non-Markovianity of the observed system and ultimately saturates toward a fixed value at a long time limit. It is worth noting that there are several appealing conclusions raised by us: First, the uncertainty’s lower bound does not entirely depend on the quantum correlations within the two-qubit system, being affected by an interplay between the quantum discord and the minimal von Neumann conditional entropy \(\mathcal{S}_\mathrm{ce}\). Second, the dynamic characteristic of the measurement uncertainty is considerably distinctive with regard to Markovian and non-Markovian regimes, respectively. Third, the measurement uncertainty is closely correlated with the Bell non-locality \({\mathcal{B}}\). Moreover, we claim that the entropic uncertainty relation could be a promising tool with which to probe entanglement in current architecture.     

Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments

Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink’s entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.     

The creation of quantum correlation and entropic uncertainty relation in photonic crystals

We investigate the dynamic creation of quantum correlation and entropic uncertainty relation (EUR) in a system of two non-interacting qubits, which are initially prepared in a classically correlated state and subject to the independent radiation in an isotropic or anisotropic photonic bandgap (PBG) crystal environment. It is shown that the detuning condition and environmental structure play a crucial role in controlling the emergence of geometric quantum discord (GQD) and one-norm GQD. In addition, the remarkable similarities and differences for quantum correlation in two PBG environments are also analyzed in detail. Finally, we explore the time evolution of EUR in our model under the influence of PBG environment and present some interesting results.     

Variance-based uncertainty relations for incompatible observables

Quantum Information Processing - We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type...     

State-independent uncertainty relations and entanglement detection

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N-dimensional observables. The uncertainty relation for the incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn’s conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.     

An entropic criterion for minimum uncertainty sensing inrecognition and localization. II. A case study on directional distancemeasurements

For pt. 1 see ibid. An entropic criterion for minimum uncertainty sensing, introduced in the companion paper, is applied to a case study related to the localization and recognition of a polygonal object by means of an orientable range finder. The observed object is characterized by two different uncertain parameters: the pose (position and orientation) of the object and its identity. A priori, only partial information is available both on the object identity and on its pose. Additional information about the observed object is acquired by the orientable range finder activated according to the above criterion.     

Exploration of entropic uncertainty relation for two accelerating atoms immersed in a bath of electromagnetic field

Quantum Information Processing - Games with unawareness model strategic situations in which players’ perceptions about the game are limited. They take into account the fact that the players...     

Stronger uncertainty relations with improvable upper and lower bounds

The quantum superposition principle is used to establish improved upper and lower bounds for the Maccone–Pati uncertainty inequality, which is based on a “weighted-like” sum of the variances of observables. Our bounds include free parameters that not only guarantee nontrivial bounds but also effectively control the bounds’ tightness. Significantly, these free parameters depend on neither the state nor the observables. A feature of our method is that any nontrivial bound can always be improved. In addition, we generalize both bounds to uncertainty relations with multiple (three or more) observables, maintaining the uncertainty relations’ tightness. Examples are given to illustrate our improved bounds.     

An entropic criterion for minimum uncertainty sensing inrecognition and localization. I. Theoretical and conceptual aspects

A criterion is presented for the automatic selection of a sensor measurement aimed at observing the state of a system which is described both by discrete variables and by continuous ones. The criterion is based on the expected value of the entropy variation associated to the sensor observation. This criterion is then applied to object recognition and localization tasks, in which the observed system is characterized by the object class, represented by a discrete variable, and by the object pose, i.e., position and orientation, represented by a vector of continuous parameters. The proposed criterion also accounts for the information obtained in the case the observed object is missed by the measurement.     

Systems with structured uncertainty: relations between quadraticand robust stability

The relation between the notions of robust stability and quadratic stability for uncertain systems with structured uncertainty due to both real and complex parameter variations is discussed. Examples are presented to demonstrate that for systems containing at least two uncertain blocks, the notions of robust stability for complex parameter variations and quadratic stability for real parameter variations are not equivalent. A byproduct of these examples is that, for this class of systems, quadratic stability for real perturbations need not imply quadratic stability for complex perturbations. This is in stark contrast with the situation in the case of unstructured uncertainty, for which it is known that quadratic stability for either real or complex perturbations is equivalent to robust stability for complex perturbations, and thus equivalent to a small gain condition on the transfer matrix that the perturbation experiences     

A View on Decoherence Via Master Equations

This paper addresses the discussion on probabilistic features of the concept of decoherence as it appeared in quantum physics. Given a Lindblad-type generator of an open system dynamics, we derive applicable criteria to characterize decoherent behaviour.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14-20, 2004.Partially supported by FONDECYT grant 1030552.     

Quantum Erasure of Decoherence

We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction, and present the generalization of the eraser setup for d-dimensional systems. Presented at the 38th Symposium on Mathematical Physics “Quantum Entanglement & Geometry”, Toruń, June 4–7, 2006.     

Generalized uncertainty principle and the Ramsauer-Townsend effect

The scattering cross-section of electrons in noble gas atoms exhibits a minimum value at electron energies of approximately 1 eV. This is the Ramsauer-Townsend effect. In this letter, we study the Ramsauer-Townsend effect in the framework of the Generalized Uncertainty Principle.     

Security portfolio management based on combined entropic risk measures

A combined entropic financial risk measure that is a convex combination of the entropic risk measure and the CVaR measure is considered. The effectiveness of the proposed measure in the formation of security portfolios is analyzed. Results of computational experiments are presented.     

LEGClust- a clustering algorithm based on layered entropic subgraphs.

Hierarchical clustering is a stepwise clustering method usually based on proximity measures between objects or sets of objects from a given data set. The most common proximity measures are distance measures. The derived proximity matrices can be used to build graphs, which provide the basic structure for some clustering methods. We present here a new proximity matrix based on an entropic measure and also a clustering algorithm (LEGClust) that builds layers of subgraphs based on this matrix, and uses them and a hierarchical agglomerative clustering technique to form the clusters. Our approach capitalizes on both a graph structure and a hierarchical construction. Moreover, by using entropy as a proximity measure we are able, with no assumption about the cluster shapes, to capture the local structure of the data, forcing the clustering method to reflect this structure. We present several experiments on artificial and real data sets that provide evidence on the superior performance of this new algorithm when compared with competing ones.     

基于链式竞争遗传算法的KSW熵的图像分割

针对最佳熵阈值图像分割算法过程中计算复杂度高的问题,提出了一种基于链式竞争遗传算法的最佳熵阈值确定法(KSW熵法)的图像分割算法.通过将3个邻域的链式竞争引入到常规遗传算法框架下,实现特征选择过程;将改进的遗传算法应用到最佳阈值图像分割算法中,完成对阈值的寻优过程.仿真实验结果与分析表明:算法在分割速度和效果上均优于传统的最佳阈值图像分割算法和单纯的遗传优化最佳阈值图像分割算法.